We propose to investigate the following three important statistical problems arising in cancer studies. The results from-this research would be quite useful in analyzing cancer studies. These problems are: 1) Semi-parametric methods for the linear regression model with censored data. We will study efficient numerical algorithms to implement the rank linear regression methods proposed by Wei, Ying, and Lin (1990) with censored data; investigate the appropriateness of the large sample theory for their procedures with practical sample sizes; generalize their methods to the multivariate failure time data; study procedures for monitoring cancer survival trials; explore linear regression methods for highly stratified failure time observations; and study the Buckley-James procedures. 2) Lack-of-fit test for regression models. We will study the lack-of-fit test proposed by Su and Wei (1990) for the correlated data; examine their methods for cases with ordinal categorical data; and study linear regression diagnostic methods with censored data. 3) Analysis of repeated order categorical response data. We will study the mixed effects model under such a data structure.